With the increasing integration of a high proportion of renewable energy sources, risk assessment for distribution systems is crucial for ensuring the safe and reliable supply of electricity. This paper reviews the progress and future prospects of risk assessment for distribution systems. First, it introduces the risk assessment methods for distribution equipment, focusing on failure rate modeling, including probability distribution fitting, machine learning, and mechanism-driven approaches, as well as consequence value calculation. Next, it summarizes the uncertainty analysis methods in distribution system risk assessment, covering analytical methods, simulation methods, approximation methods, and machine learning methods, along with evaluation indicators such as reliability, vulnerability, and power quality, and their comprehensive evaluation methods. Finally, based on the above analysis and summary, the future development directions of risk assessment technology for distribution systems are discussed.